Quark scalar, axial and tensor charges in the Schwinger-Dyson formalism

TL;DR

This paper calculates the quark scalar, axial, and tensor charges of the nucleon using the Schwinger-Dyson formalism, comparing different truncation schemes and highlighting the need for further corrections in the deep IR region.

Contribution

It demonstrates the calculation of nucleon charges within the Schwinger-Dyson approach and analyzes the effects of different quark-gluon vertex models on the results.

Findings

Rainbow-ladder truncation yields results consistent with known data.

Phenomenological IR singular vertex causes non-convergence of equations.

Additional IR corrections are necessary for accurate modeling.

Abstract

The quark scalar, axial and tensor charges of nucleon are calculated in the Schwinger-Dyson formalism. We first calculate these charges in the rainbow-ladder truncation using the IR cut quark-gluon vertex, and show that the result is in agreement with the known data. We then perform the same calculation with the phenomenological IR singular quark-gluon vertex. In this case, the Schwinger-Dyson equation does not converge. We show that this result suggests the requirement of additional corrections to the rainbow-ladder truncation, due to the interaction between quark and gluons in the deep IR region.